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2.9 Summary

The future linear $\mbox{${{e}}^+ {{e}}^-$ }$ collider, JLC, gives us fantastic occasions to investigate the physics up to GUT scale through studies of Higgs production and decay properties.

In this report we studied varieties of Higgs physics based on the recent progress in theoretical and experimental sides.

The experimental feasibilities and sensitivities are investigated especially for physics at early stage of the JLC phase-I. We discussed the sensitive signal cross-section, model-independent measurements, and expected accuracy in physics parameters such as Yukawa-coupling. Full simulation studies for the tracking as well as the effect of the event overlapping expected at JLC has been started already.

The existence of the light Higgs predicted in SUSY models is first to be clarified. At JLC, we may need only a few days to discover (at least one of) the Higgs bosons if the current design luminosity value of JLC is realized. There is always a potential for us to find unexpected ``big things'' through Higgs hunting and measurements even at very early stage of the JLC experiment.

We have enough sensitivity even to the worst case with the lowest cross-section in SUSY models. The physics background processes which have event topologies similar to those of Higgs signals have cross-section just one or two orders of magnitude higher than the signal. The backgrounds are well under control thanks to the well defined initial states, which is necessary for the precise measurement of the Higgs and in order to be sensitive to new particle production with tiny cross-section. We are sensitive to a cross-section down to 1 fb level. One can say, in other words, it is really a ``big discovery'' when we find no Higgs at JLC phase-I.

Varieties of discoveries are yet waiting for us. For instance, if Br $(\mbox{${h}^{0}$ }\mbox{$\rightarrow$ }\mbox{${b}\bar{{b}}$ })$/Br $(\mbox{${h}^{0}$ }\mbox{$\rightarrow$ }\tau\tau)$ is found to be different from $m_{b}^2/m_{\tau}^2$, all models belonging to SM or type-II 2HDM, such as SUSY models, are excluded. If Yukawa couplings of top and charm normalized to its mass are found to be different, we need completely new theory for the fermion generation. If the measured cross-section is smaller than the minimum cross-section [11,12] expected in SUSY models, it means new physics further beyond SUSY between EW and GUT scale. We may discover CP-mixing in Higgs sector. We also may discover other Higgs with tiny cross-section at JLC even at phase-I.

Our purpose of the experiments at JLC is not only to judge the existence of the light Higgs, but also to measure the Higgs properties precise enough if it exists. We would measure the cross-section, the branching ratio, natural width in percent order or less in its error at JLC based on more than 105 Higgs events in a few years running which results in the precise measurements of the Higgs gauge coupling and Yukawa-coupling, and furthermore derivation of Higgs self-couplings in multi-Higgs production. These can be made model independent fashion.

From these measurements, we further measure various model parameters, and test in the internal consistency. The precise values of the Higgs properties, we are also sensitive to a loop effect of new particles such as scaler top quark. The mass of the other Higgs and properties are indirectly measured if we missed it at JLC phase-I, and can be tested at the next step of the JLC. The information from LHC are also helpful. All of those, which are expected to be done only with the next e+e-Linear Collider, JLC, are essential to give definite answers to physics models and to determine the fundamental structure of the interaction in nature up to GUT scale. JLC is a big step to definitely answer the question whether we live in SUSY world or SM-like world, or completely new unexpected world.

Table 2.11: Accuracy at $\sqrt {s}=$300, 400 and 500 GeV with ${\cal {L}}$=500 fb-1 for 120 GeV CP-even Higgs at JLC. The Higgs boson of SM-like is used as an input.
$\sqrt {s}$ 300 GeV 400 GeV 500 GeV
$\Delta\mbox{$m_{{h}}$ }$ (lepton-only) 80 MeV -- --
$\Delta\mbox{$m_{{h}}$ }$ 40 MeV -- --
$\Delta\sigma / \sigma$ (lepton-only) 2.1% 2.5% 2.9%
$\Delta\sigma / \sigma$ 1.3% -- --
$\Delta(\sigma_{h\nu \bar{\nu}}\cdot$Br( $\mbox{${b}\bar{{b}}$ }$) 2.0% -- --
ZZH-coupling $\Delta $ZZH/ZZH 1.1% 1.3% 1.5%
WWH-coupling $\Delta $WWH/WWH 1.6% -- --
$\Delta\Gamma_{\mbox{${h}^{0}$ }}/\Gamma_{\mbox{${h}^{0}$ }}$ 5.5% 12% 16%
Yukawa coupling $\Delta\lambda/\lambda$      
$\lambda _b$ 2.8% 6.1% 8.1%
$\lambda_{\tau}$ 3.5% -- --
$\lambda_{c}$ 11.3% 13% 15%
$\lambda_{b}/\lambda_{\tau}$ 2.3% -- --
$\lambda_{b}/\lambda_{c}$ 11% 12% 14%
$\lambda_{up-type}$ 4.1% -- --
$\lambda_{down-type}/\lambda_{up-type}$ 3.2% -- --
$\Delta(\sigma\cdot$Br)/ $(\sigma\cdot$Br)      
$\mbox{${h}^{0}$ }\mbox{$\rightarrow$ }\mbox{${b}\bar{{b}}$ }$ 1.1% 1.3% 1.7%
$\mbox{${h}^{0}$ }\mbox{$\rightarrow$ }\mbox{${W}^+{W}^-$ }$ 5.1% 12% 16%
$\mbox{${h}^{0}$ }\mbox{$\rightarrow$ }\mbox{$\tau^+\tau^-$ }$ 4.4% -- --
$\mbox{${h}^{0}$ }\mbox{$\rightarrow$ }\mbox{${c}\bar{{c}}$ }$+gg 6.3% -- --
$\mbox{${h}^{0}$ }\mbox{$\rightarrow$ }\mbox{${c}\bar{{c}}$ }$ 22% 23% 27%
$\mbox{${h}^{0}$ }\mbox{$\rightarrow$ }$gg 10% 11% 13%
$\mbox{${h}^{0}$ }\mbox{$\rightarrow$ }\gamma\gamma$ -- -- --
$\mbox{${h}^{0}$ }\mbox{$\rightarrow$ }\mbox{${Z}^{0}$ }\gamma$ -- -- --

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ACFA Linear Collider Working Group